Question: The equation of a circle $C$ is $x^2+y^2-10x-18y+97 = 0$. What is its center $(h, k)$ and its radius $r$ ?
To find the equation in standard form, complete the square. $(x^2-10x) + (y^2-18y) = -97$ $(x^2-10x+25) + (y^2-18y+81) = -97 + 25 + 81$ $(x-5)^{2} + (y-9)^{2} = 9 = 3^2$ Thus, $(h, k) = (5, 9)$ and $r = 3$.